Foundation models pretrained on various and unlabeled data have demonstrated significant success in natural language and vision, but their application to electroencephalography (EEG) remains challenged due to the signal's unique properties. Existing brain foundation models that inherit architectures designed for text or images lead to three limitations in pre-training: 1) conflating time-domain waveform patterns with frequency-domain rhythmic features in a single processing stream, 2) ignoring the critical spatial topology of electrodes with different standards, and 3) reliance on the inflexible, dense network to process functionally distinct EEG patterns. To address these challenges, we introduce the Unified Neural Topological Foundation Model (Uni-NTFM), which is designed based on neuroscience principles to produce universal and interpretable representations. Uni-NTFM integrates three core innovations: 1) a decoupled architecture parallelly encodes time, frequency, and raw signal representations before performing cross-domain feature integration; 2) a topological embedding mechanism to unify electrodes from different international standards and generate structured input sequences for brain regions; and 3) a Mixture-of-Experts neural Transformer that efficiently scales model capacity by routing signal patterns to specialized subnetworks. The largest model, Uni-NTFM$_{large}$, has a record-breaking 1.9B parameters and was pretrained on over 28,000 hours of diverse EEG data via a dual-domain masked reconstruction objective. Uni-NTFM significantly outperforms existing task-specific methods and foundation models across nine distinct downstream tasks under both linear probing and fine-tuning settings, demonstrating a superior ability to learn universal representations of brain activity.

Classification models typically predict a score and use a decision threshold to produce a classification. Appropriate model evaluation should carefully consider the context in which a model will be used, including the relative value of correct classifications of positive versus negative examples, which affects the threshold that should be used. Decision curve analysis (DCA) and cost curves are model evaluation approaches that assess the expected utility and expected loss of prediction models, respectively, across decision thresholds. We compared DCA and cost curves to determine how they are related, and their strengths and limitations. We demonstrate that decision curves are closely related to a specific type of cost curve called a Brier curve. Both curves are derived assuming model scores are calibrated and setting the classification threshold using the relative value of correct positive and negative classifications, and the x-axis of both curves are equivalent. Net benefit (used for DCA) and Brier loss (used for Brier curves) will always choose the same model as optimal at any given threshold. Across thresholds, differences in Brier loss are comparable whereas differences in net benefit cannot be compared. Brier curves are more generally applicable (when a wider range of thresholds are plausible), and the area under the Brier curve is the Brier score. We demonstrate that reference lines common in each space can be included in either and suggest the upper envelope decision curve as a useful comparison for DCA showing the possible gain in net benefit that could be achieved through recalibration alone.

Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to identify dynamic ranking groups by incorporating temporal penalties into a spectral estimation for the celebrated Bradley-Terry model. To detect structural changes, we introduce an innovative objective function and present a practicable algorithm based on dynamic programming. Theoretically, we establish the consistency of ranking group recognition by exploiting properties of a random `design matrix' induced by a reversible Markov chain. We also tailor a group inverse technique to quantify the uncertainty in item ability estimates. Additionally, we prove the consistency of structure change recognition, ensuring the robustness of the proposed framework. Experiments on both synthetic and real-world datasets demonstrate the practical utility and interpretability of our approach.

The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we argue that the various classes come from different probability distributions. The localized kernel technique developed for separating point sources is then shown to separate the supports of these distributions. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. We illustrate our theory on several simulated and real life datasets, including the Salinas and Indian Pines hyperspectral datasets and a document dataset.

As machine learning (ML) algorithms are increasingly used in social domains to make predictions about humans, there is a growing concern that these algorithms may exhibit biases against certain social groups. Numerous notions of fairness have been proposed in the literature to measure the unfairness of ML. Among them, one class that receives the most attention is \textit{parity-based}, i.e., achieving fairness by equalizing treatment or outcomes for different social groups. However, achieving parity-based fairness often comes at the cost of lowering model accuracy and is undesirable for many high-stakes domains like healthcare. To avoid inferior accuracy, a line of research focuses on \textit{preference-based} fairness, under which any group of individuals would experience the highest accuracy and collectively prefer the ML outcomes assigned to them if they were given the choice between various sets of outcomes. However, these works assume individual demographic information is known and fully accessible during training. In this paper, we relax this requirement and propose a novel \textit{demographic-agnostic fairness without harm (DAFH)} optimization algorithm, which jointly learns a group classifier that partitions the population into multiple groups and a set of decoupled classifiers associated with these groups. Theoretically, we conduct sample complexity analysis and show that our method can outperform the baselines when demographic information is known and used to train decoupled classifiers. Experiments on both synthetic and real data validate the proposed method.

The Mixture-of-Experts (MoE) architecture has enabled the creation of massive yet efficient Large Language Models (LLMs). However, the standard deterministic routing mechanism presents a significant limitation: its inherent brittleness is a key contributor to model miscalibration and overconfidence, resulting in systems that often do not know what they don't know. This thesis confronts this challenge by proposing a structured \textbf{Bayesian MoE routing framework}. Instead of forcing a single, deterministic expert selection, our approach models a probability distribution over the routing decision itself. We systematically investigate three families of methods that introduce this principled uncertainty at different stages of the routing pipeline: in the \textbf{weight-space}, the \textbf{logit-space}, and the final \textbf{selection-space}. Through a series of controlled experiments on a 3-billion parameter MoE model, we demonstrate that this framework significantly improves routing stability, in-distribution calibration, and out-of-distribution (OoD) detection. The results show that by targeting this core architectural component, we can create a more reliable internal uncertainty signal. This work provides a practical and computationally tractable pathway towards building more robust and self-aware LLMs, taking a crucial step towards making them know what they don't know.

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework for statistical inference in gradient boosting regression. Our framework integrates dropout or parallel training with a recently proposed regularization procedure that allows for a central limit theorem (CLT) for boosting. With these enhancements, we surprisingly find that increasing the dropout rate and the number of trees grown in parallel at each iteration substantially enhances signal recovery and overall performance. Our resulting algorithms enjoy similar CLTs, which we use to construct built-in confidence intervals, prediction intervals, and rigorous hypothesis tests for assessing variable importance. Numerical experiments demonstrate that our algorithms perform well, interpolate between regularized boosting and random forests, and confirm the validity of their built-in statistical inference procedures.

Recent advances in deep learning highlight the need for personalized models that can learn from small or moderate samples, handle high dimensional features, and remain interpretable. To address this challenge, we propose the Sparse Deep Additive Model with Interactions (SDAMI), a framework that combines sparsity driven feature selection with deep subnetworks for flexible function approximation. Unlike conventional deep learning models, which often function as black boxes, SDAMI explicitly disentangles main effects and interaction effects to enhance interpretability. At the same time, its deep additive structure achieves higher predictive accuracy than classical additive models. Central to SDAMI is the concept of an Effect Footprint, which assumes that higher order interactions project marginally onto main effects. Guided by this principle, SDAMI adopts a two stage strategy: first, identify strong main effects that implicitly carry information about important interactions. second, exploit this information through structured regularization such as group lasso to distinguish genuine main effects from interaction effects. For each selected main effect, SDAMI constructs a dedicated subnetwork, enabling nonlinear function approximation while preserving interpretability and providing a structured foundation for modeling interactions. Extensive simulations with comparisons confirm SDAMI$'$s ability to recover effect structures across diverse scenarios, while applications in reliability analysis, neuroscience, and medical diagnostics further demonstrate its versatility in addressing real-world high-dimensional modeling challenges.

Abstract--In machine learning, uncertainty quantification helps assess the reliability of model predictions, which is important in high-stakes scenarios. Traditional approaches often emphasize predictive accuracy, but there is a growing focus on incorporating uncertainty measures. While current methods often rely on quantile regression or Monte Carlo techniques, we propose a new approach using naturally occurring test sets and similarity measures (proximities) typically viewed as byproducts of random forests. Specifically, we form localized distributions of OOB errors around nearby points, defined using the proximities, to create prediction intervals for regression and trust scores for classification. By varying the number of nearby points, our intervals can be adjusted to achieve the desired coverage while retaining the flexibility that reflects the certainty of individual predictions. For classification, excluding points identified as unclassifiable by our method generally enhances the accuracy of the model and provides higher accuracy-rejection AUC scores than competing methods. Although traditional machine learning models usually provide point estimates, there is growing recognition of the need to incorporate uncertainty to support more informed decisions [1]. By quantifying uncertainty, users can assess the reliability of model outputs and better interpret results, especially for out-of-distribution samples through calibrated confidence estimates.

Online controlled experiments (A/B tests) are fundamental to data - driven decision - making in the digital economy. However, their real - world application is frequently compromised by two critical shortcomings: the use of statistically flawed heuristics like " p - value peeking", which inflates false positive rates, and an over - reliance on proxy metrics like conversion rates, which can lead to decisions that inadvertently harm core business profitability. This paper addresses these challenges by introducing a comp rehensive and scalable Bayesian decision framework designed for profit optimization in multi - variant (A/B/n) experiments. We propose a hierarchical Bayesian model that simultaneously estimates the probability of conversion (using a Beta - Bernoulli model) and the monetary value of that conversion (using a robust Bayesian model for the mean transaction value). Building on this, we employ a decision - theoretic stopping rule based on Expected Loss, enabling experiments to be concluded not only when a superior variant is identified but also when it becomes clear that no variant offers a practically significant improvement (stopping f or futility). The framework successfully navigates "revenue traps" where a variant with a higher conversion rate would have resulted in a net financial loss, correctly terminates futile experiments early to conserve resources, and maintains strict statisti cal integrity throughout the monitoring process. Ultimately, this work provides a practical and principled methodology for organizations to move beyond simple A/B testing towards a mature, profit - driven experimentation culture, ensuring that statistical conclusions translate directly to strategic busines s value.